No, it's not a bug at all. Use the option AxesOrigin so that it is consistent with the region to be plotted. (BTW, this doesn't seem to alleviate the ugliness of the plot). E.g.Plot[Abs[Zeta[1/2 + I*t]/t^(1/4)], {t, 35000, 50000}, AxesOrigin -> {35000, 0}, PlotRange -> Full]-Tomas